The following points not clearly understandable, could you please help me to make it clear.
The major effects with the presence of a CPL in a dc power system are as follows
1. Reduces the equivalent resistance of the system.
2. Causes high inrush current, as voltage build-up slowly from its initial value.
3. Reduces system damping and stability margins.
4. Causes limit cycle oscillation in the dc bus voltage and currents.
5. May lead to voltage collapse.
For constant power load, if, V and I be the voltage across and current through the load, then, V*I = constant. And then, V. dI + I. dV = 0; or, dynamic resistance dV/dI = -V/I. V/I is the static resistance. You can note that dynamic resistance is negative.
You also know that resistance of a circuit determines the damping of a circuit. Effective reduction of dynamic resistance reduces system damping, and in a way will reduce stability margin.For example, in a RLC series circuit, transient response can be given by, Ld2i/dt2 + Rdi/dt+ i/C = delta(t). Rdi/dt is responsible for damping. If R reduces, effective damping reduces. If, R = 0, the system will show oscillatory response (similar to limit cycle). If, R < 0 damping will be negative, i.e., real part of the system poles will become positive, and system will lose its stability.
Large inrush current can also be explained similarly. For example, because VI = constant, if V = 0, I will be undefined. Once you connect such load into a DC grid, it will draw large current from the circuit because of reflection of voltage and current wave.
For constant power load, if, V and I be the voltage across and current through the load, then, V*I = constant. And then, V. dI + I. dV = 0; or, dynamic resistance dV/dI = -V/I. V/I is the static resistance. You can note that dynamic resistance is negative.
You also know that resistance of a circuit determines the damping of a circuit. Effective reduction of dynamic resistance reduces system damping, and in a way will reduce stability margin.For example, in a RLC series circuit, transient response can be given by, Ld2i/dt2 + Rdi/dt+ i/C = delta(t). Rdi/dt is responsible for damping. If R reduces, effective damping reduces. If, R = 0, the system will show oscillatory response (similar to limit cycle). If, R < 0 damping will be negative, i.e., real part of the system poles will become positive, and system will lose its stability.
Large inrush current can also be explained similarly. For example, because VI = constant, if V = 0, I will be undefined. Once you connect such load into a DC grid, it will draw large current from the circuit because of reflection of voltage and current wave.
Dear Mohamed
I am considering the constant power load as the DC-DC load converter for voltage regulation purposes, and DC –AC inverter for speed regulation purposes.
The use of constant power load is recommended to simulate loads that represent induction motors. They can thus be represented up to 80% of the rated voltage normally.
Dear Sanjay Huse
you can get the paper attached below, to understand clearly what is the effect of constant power load(CPL) on the stability of the cascading power switching converters.
I hope it helps you
Thanks
Dear Subir Majumder
Thanks for your explanation, as you mentioned for series RLC, if R=0 the system loosing the damping, and the energy will oscillate between capacitor and inductor. But in case of parallel RLC circuit maybe vice versa, in case of R=0 is the best situation for damping all of the energy in the circuit. are agree with me?
Thanks
Truly Yours
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